Least Common Multiple of 969 and 972

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 969 and 972 the smallest integer that is 313956 that is divisible by both numbers.

Least Common Multiple (LCM) of 969 and 972 is 313956.

LCM(969,972) = 313956

LCM of 969 and 972

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 969 and 972

LCM of 969 and 972 is 313956

Least common multiple can be found by multiplying the highest exponent prime factors of 969 and 972. First we will calculate the prime factors of 969 and 972.

Prime Factorization of 969


3 969
17 323
19 19
1

Prime factors of 969 are 3, 17,19. Prime factorization of 969 in exponential form is:

969 = 31×171×191

Prime Factorization of 972


2 972
2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 972 are 2,3. Prime factorization of 972 in exponential form is:

972 = 22×35

Now multiplying the highest exponent prime factors to calculate the LCM of 969 and 972.

LCM(969,972) = 22×35×171×191
LCM(969,972) = 313956

Factors of 969

List of positive integer factors of 969 that divides 969 without a remainder.

1, 3, 17, 19, 51, 57, 323, 969

Factors of 972

List of positive integer factors of 972 that divides 972 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972

Least Common Multiple of 969 and 972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 969 and 972, than apply into the LCM equation.

GCF(969,972) = 3
LCM(969,972) = ( 969 × 972) / 3
LCM(969,972) = 941868 / 3
LCM(969,972) = 313956

Properties of LCM 969 and 972

(i) The LCM of 972 and 969 is associative

LCM of 969 and 972 = LCM of 972 and 969

Related Least Common Multiples of 969

Related Least Common Multiples of 972

Frequently Asked Questions on LCM of 969 and 972

1. What is the LCM of 969 and 972?

Answer: LCM of 969 and 972 is 313956.

2. What are the Factors of 969?

Answer: Factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969. There are 8 integers that are factors of 969. The greatest factor of 969 is 969.

3. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

4. How to Find the LCM of 969 and 972?

Answer:

Least Common Multiple of 969 and 972 = 313956

Step 1: Find the prime factorization of 969

969 = 3 x 17 x 19

Step 2: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 313956 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 17 x 19

Step 4: Therefore, the least common multiple of 969 and 972 is 313956.